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研究生： 李東璋
Li, Tung-Chang
論文名稱： 在三個非重複字串上的最長共同子字串
Longest common substring on non repetitive three strings
指導教授： 林瀚仚
Lin, Han-Hsuan
口試委員: 韓永楷
Hon, Wing-Kai
賴青沂
Lai, Ching-Yi
學位類別： 碩士
Master
系所名稱： 電機資訊學院 - 資訊工程學系
Computer Science
論文出版年： 2023
畢業學年度： 112
語文別： 英文
論文頁數： 17
中文關鍵詞： 量子演算法 、字串 、最長公共子字串 、非重複
外文關鍵詞： string, non-repetitive
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    • 字串演算法是一個重要的研究領域，可應用於許多領域。 在此背景下，我們深入研究了在三個字串中尋找最長公共子字串的問題，這個問題可以用基於後綴樹的經典演算法在線性時間內完成。在本文中，我們提出可以在tilde{O}(n^{5/6})時間內完成三個字串的量子版本的最長公共子字串。

    String algorithms are an important area of research and can be applied in many fields. In this context, we delve into the issue of finding the longest common substring among three strings, which can be accomplished in linear time using a classical algorithm based on suffix trees. In this work we propose that the longest common substring of the quantum version of the three strings can be solved in tilde{O}(n^{5/6}) time.

    Abstract(Chinese) I Acknowledgements(Chinese) II Abstract III Acknowledgements IV Contents V 1 Introduction 1 2 Preliminaries 4 2.1 Problem 4 2.2 Basic Quantum Primitives 4 2.3 Markov chain 6 2.4 Quantum Walk 7 3 Longest Common Subsrting for Non-repetitive Three Strings 9 3.1 Non repetitive LCS algorithm for small d 9 3.2 Non repetitive LCS algorithm for large d 13 3.3 Combining the two algorithm 14 Bibliography 16

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